Related papers: Radial Evolution in a Reaction-Diffusion Model
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes…
The studies of fluctuations of the one-dimensional Kardar-Parisi-Zhang universality class using the techniques from random matrix theory are reviewed from the point of view of the asymmetric simple exclusion process. We explain the basics…
Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction…
Subdiffusion with reaction $A+B\rightarrow B$ is considered in a system which consists of two homogeneous media joined together; the $A$ particles are mobile whereas $B$ are static. Subdiffusion and reaction parameters, which are assumed to…
We study random velocity effects on a two-species reaction-diffusion system consisting of three reaction processes $A + A \rightarrow (\varnothing, A),A+B \rightarrow A$. Using the field-theoretic perturbative renormalization group we…
We use a boolean cellular automaton model to describe the diffusion limited dynamics of the irreversible reaction A+A->A+S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which…
We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The…
We have used kinetic Monte Carlo (kMC) simulations of a lattice gas to study front fluctuations in the spreading of a non-volatile liquid droplet onto a solid substrate. Our results are consistent with a diffusive growth law for the radius…
Using the quasistatic approximation, we show that in a subdiffusion--reaction system the reaction front $x_{f}$ evolves in time according to the formula $x_{f} \sim t^{\alpha/2}$, with $\alpha$ being the subdiffusion parameter. The result…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…
Spiral waves emerge in numerous pattern forming systems and are commonly modeled with reaction-diffusion systems. Some systems used to model biological processes, such as ion-channel models, fall under the reaction-diffusion category and…
A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate…
We formulate the theory for a self-propelled domain in an excitable reaction-diffusion system in two dimensions where the domain deforms from a circular shape when the propagation velocity is increased. In the singular limit where the width…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
The combination of protrusions and retractions in the movement of polarized cells leads to understand the effect of possible synchronisation between the two ends of the cells. This synchronisation, in turn, could lead to different dynamics…
The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…
We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially…
A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$.…